Abstract

Accurate prediction of muscle and joint contact forces during human movement could improve treatment planning for disorders such as osteoarthritis, stroke, Parkinson's disease, and cerebral palsy. Recent studies suggest that muscle synergies, a low-dimensional representation of a large set of muscle electromyographic (EMG) signals (henceforth called “muscle excitations”), may reduce the redundancy of muscle excitation solutions predicted by optimization methods. This study explores the feasibility of using muscle synergy information extracted from eight muscle EMG signals (henceforth called “included” muscle excitations) to accurately construct muscle excitations from up to 16 additional EMG signals (henceforth called “excluded” muscle excitations). Using treadmill walking data collected at multiple speeds from two subjects (one healthy, one poststroke), we performed muscle synergy analysis on all possible subsets of eight included muscle excitations and evaluated how well the calculated time-varying synergy excitations could construct the remaining excluded muscle excitations (henceforth called “synergy extrapolation”). We found that some, but not all, eight-muscle subsets yielded synergy excitations that achieved >90% extrapolation variance accounted for (VAF). Using the top 10% of subsets, we developed muscle selection heuristics to identify included muscle combinations whose synergy excitations achieved high extrapolation accuracy. For 3, 4, and 5 synergies, these heuristics yielded extrapolation VAF values approximately 5% lower than corresponding reconstruction VAF values for each associated eight-muscle subset. These results suggest that synergy excitations obtained from experimentally measured muscle excitations can accurately construct unmeasured muscle excitations, which could help limit muscle excitations predicted by muscle force optimizations.

Figures

Overview of synergy extrapolation approach. All possible combinations of eight surface EMG measurements were identified and labeled as the included muscle subsets for each full data set (healthy, stroke nonparetic leg, stroke paretic leg). Synergy analysis was performed on each included subset to determine a set of three to five time-varying synergy excitations that reconstructed the eight surface EMG signals. The subset of remaining muscle excitations not included in the synergy analysis was labeled as the excluded muscle subset and was fitted with the extracted synergy excitations through linear least-squares regression. The constructed excluded muscle excitations were compared to the experimental excluded muscle excitations using VAF calculations. VAF values were averaged across muscles and gait cycles to create a single extrapolation VAF value for each included–excluded muscle subset pair. This synergy extrapolation approach was repeated for each walking speed of all three data sets.

Percentage of included muscle combinations that achieved a specified extrapolation VAF value (80%, 85%, or 90%) for the healthy subject (top), the nonparetic leg of the stroke subject (middle), and the paretic leg of the stroke subject (bottom) across all walking speeds. Extrapolation VAF results were generated using five synergy excitations. Extrapolation ability varied across walking speeds, but no consistent trend appeared across the three data sets. The percentage of acceptable muscle combinations changed significantly with relatively small changes in VAF cutoff value. For these results in absolute numbers instead of percentage values, refer to Table 2.

Mean extrapolation VAF for the top 10% of combinations averaged across walking trials (black circles) for the healthy subject (left), the nonparetic leg of the stroke subject (middle), and the paretic leg of the stroke subject (right) using three to five synergies. Error bars representing plus or minus one standard deviation demonstrate the variability across walking trials for each data set. Reference lines represent VAF cutoff values for typical synergy analyses (90% and 95%). Using five synergies, all three data sets achieved on average a mean extrapolation VAF of 90% or greater across all walking speeds. The paretic leg data set exhibited a reduced extrapolation ability with more variability across walking speeds compared to the nonparetic leg and the healthy data sets.

Comparison of reconstructed and experimental (black) muscle excitations for (a) eight included muscle excitations and (b) eight excluded muscle excitations using three (red), four (green), and five (blue) synergies. Sample EMG data were taken from the paretic leg of the stroke subject walking at 0.7 m/s. The included muscle excitations were selected based on the previously described muscle selection heuristics and were reconstructed using the synergy excitations and synergy vectors obtained from synergy analysis. The excluded muscle excitations were reconstructed using the synergy excitations obtained from the included muscles and our linear least-squares implementation of synergy extrapolation. VAF values for each reconstructed muscle excitation are provided in Table 6.

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